1. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Lesson 26:Percent of a Quantity
Student Outcomes

Students find the percent of a quantity. Given a part and the percent, students solve problems involving
finding the whole.
Classwork
Example 1 (5 minutes)
Example 1
Five of the
girls on Alden Middle School’s soccer team are 7th-grade students. Find the percentage of 7th graders on the
team. Show two different ways of solving for the answer. One of the methods must include a diagram or picture model.
Method 1
0%
20%
0
5
40%
60%
10
15
80% 100%
20
25
Method 2
Students take time to make their own diagram or model and discuss with a partner. Students will be reviewing the work
they completed in Lesson 25. If they made a tape diagram, they begin by deciding to divide the tape diagram into 5 equal
rectangles. Each rectangle will represent 5 girls. From there they will need to divide the 100% into 5 equal sections.
If time permits, students share the model they chose and explain why it did or did not help them solve the question.
Students need to come to the conclusion that
=
, which is the same as 20%.
Note: Students whoare struggling may need help figuring out which model to use and how to divide up the diagram.
Help them think through the different options. Would it make sense to count by 5s, 10s, 20s, 25s, etc.?
Lesson 26:
Date:
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Percent of a Quantity
11/14/13
207
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2. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Example 2 (5 minutes)
Example 2
Of the
girls on the Alden Middle School soccer team,
middle school team also play on a travel team?
One method:
Therefore,
of the
also play on a travel team. How many of the girls on the
are on the travel team.
Another method: Use of tape diagram shown below.
0%
0
20%
40%
5
10
60%
15
80%
20
100%
25
10 of the girls also play on a travel team.
Example 3 (5 minutes)
Example 3
The Alden Middle School girls’ soccer team won
of their games this season. If the team won
games did they play? Solve the question using at least two different methods.
games, how many
Method 1:
15 total games
Method 2:
0%
0
20%
40%
60%
3
6
9
80%
12
100%
15
The girls played a total of 15 games.
Lesson 26:
Date:
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Percent of a Quantity
11/14/13
208
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3. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Exercises 1–4(20 minutes)
At this time, the students break out into pairs or small thinking groups to solve the problems.
Exercises 1–4
1.
There are 60 animal exhibits at the local zoo. What percent of the zoo’s exhibits does each animal class represent?
Exhibits by Animal Class
Mammals
15
Fish & Insects
12
Birds
2.
30
Reptiles & Amphibians
3
A sweater is regularly
a.
Percent of the Total
Number of Exhibits
Number of Exhibits
. It is
off the original price this week.
Would the amount the shopper saved be considered the part, whole or percent?
Part because the
b.
is the whole amount of the sweater, and we want to know the part that was saved.
How much would a shopper save by buying the sweater this week? Show two methods for finding your
answer.
Method 1:
Method 2:
0
8
16
24
32
0
25%
50%
75%
100%
The shopper would save
3.
A pair of jeans was
a.
.
off the original price. The sale resulted in a
discount.
Is the original price of the jeans considered the whole, part or percent?
The original price is the whole.
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Date:
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Percent of a Quantity
11/14/13
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4. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
b.
6•1
What was the original cost of the jeans before the sale?Show two methods for finding your answer.
Method 1:
The original cost was
.
Method 2:
0
80
16
24
32
40
48
56
64
72
0
100
4.
8
10
20
30
40
50
60
70
80
90
Purchasing a TV that is
a.
off will save
.
Name the different parts with the words: PART, WHOLE, PERCENT.
PERCENTPART
WHOLE
20% off
b.
$180
Original Price
What was the original price of the TV?Show two methods for finding your answer.
Method 1:
0%
0
10%
20%
90
180
30%
40%
270 360
450
50%
540
60%
630
70%
80%
720
90%
810
100%
900
Method 2:
The original price was $900.
Lesson 26:
Date:
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Percent of a Quantity
11/14/13
210
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5. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Closing (10 minutes)

Describe additional questions.

Discuss the main differences in solving strategies.

Were there times when you preferred to use one method over another method?

How did the steps change when you were given the part instead of the total?
Lesson Summary
Models and diagrams can be used to solve percent problems. Tape diagrams,
grids, double number line
diagrams, and others can be used in a similar way to using them with ratios to find the percent, the part or the
whole.
Exit Ticket (5 minutes)
Lesson 26:
Date:
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Percent of a Quantity
11/14/13
211
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6. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
6•1
Date____________________
Lesson 26: Percent of a Quantity
Exit Ticket
1.
Find
of
using two different strategies, one of which must include a pictorial model or diagram.
2.
of an amount is 30. Calculate the whole amount using two different strategies, one of which must include a
pictorial model.
Lesson 26:
Date:
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Percent of a Quantity
11/14/13
212
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7. Lesson 26
NYS COMMON CORE MATHEMATICS CURRICULUM
6•1
Exit Ticket Sample Solutions
The following solutions indicate an understanding of the objectives of this lesson:
1.
Find
of
using two different strategies, one of which must include a pictorial model or diagram.
40% of 60 40% =
2.
=
=
40% of 60 is 24.
of an amount is 30. Calculate the whole amount using two different strategies, one of which must include a
pictorial model.
15% =
=
The whole quantity is 200.
Problem Set Sample Solutions
1.
What is 15% of 60? Create a model to prove your answer.
9
2.
If 40% of a number is 56, what was the original number?
140
3.
In a
grid that represents 800, one square represents
8
.
Use the grids below to represent 17% and 83% of 800.
17%
83%
17% of 800 is_______136________.
Lesson 26:
Date:
©2013CommonCore,Inc. Some rights reserved.commoncore.org
83% of 800 is_______ 664________.
Percent of a Quantity
11/14/13
213
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